Cedars also known as Arborvitae are often multi stemmed. It normally takes one year of recover for every year of trunk diameter, so this one plant may not be thriving as well as the others. If the needles are browned and the twigs and stems and trunk remain green just underneath the bark, wait and see what happens next year or if the stems are brown beneath the surface, the branch is likely already dead and removing it allows sunlight in to promote new growth of the remaining live branches.
